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Keywords:
boundedness; Calderón-Zygmund singular integral operator; para-product; spaces of homogeneous type
boundedness; Calderón-Zygmund singular integral operator; para-product; spaces of homogeneous type
Summary:
We obtain the boundedness of Calderón-Zygmund singular integral operators $T$ of non-convolution type on Hardy spaces $H^p(\mathcal X)$ for $ 1/{(1+\epsilon )}<p\le 1$, where ${\mathcal X}$ is a space of homogeneous type in the sense of Coifman and Weiss (1971), and $\epsilon $ is the regularity exponent of the kernel of the singular integral operator $T$. Our approach relies on the discrete Littlewood-Paley-Stein theory and discrete Calderón's identity. The crucial feature of our proof is to avoid atomic decomposition and molecular theory in contrast to what was used in the literature.
References:
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